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Doppler’s Effect of Light

The phenomenon of apparent change in frequency (or wavelength) of the light due to relative motion between the source of light and the observer is called Doppler’s effect.
 
If v = actual frequency, v’= apparent frequency, v = speed of source wrt stationary observer, c = speed of light.

Source of light moves towards the stationary observer

When a light source is moving towards an observer with a relative velocity v, then the apparent frequency (v’) is greater than the actual frequency (v) of light. Thus apparent wavelength (λ’) is lesser the actual wavelength (λ).
 
94871.png and 94878.png
 
For v << c
  • Apparent frequency, 94886.png
  • Apparent wavelength, 94892.png
  • Doppler’s shift: Apparent wavelength < actual wavelength,
     
    So spectrum of the radiation from the source of light shifts towards the violet end of spectrum. This is called violet shift
     
    Doppler’s shift, 94898.png 
  • The fraction decrease in wavelength 94908.png

Source of light moves away from the stationary observer

In this case, v’ < v and λ’ > λ
 
94914.png and 94920.png
 
For v << c
  • Apparent frequency, 94926.png
  • Apparent wavelength, 94944.png
  • Doppler’s shift: Apparent wavelength > actual wavelength,
     
    So spectrum of the radiation from the source of light shifts towards the red end of spectrum. This is called red shift
     
    Doppler’s shift, 94950.png
  • The fractional increase in wavelength 94960.png

Doppler broadening

For a gas in a discharge tube, atoms are moving randomly in all directions. When spectrum of light emitted from these atoms is analyzed, then due to Doppler effect (because some atoms are moving towards detector, some atoms are moving away from detector), the frequency of a spectral line is not observed as having one value, but is spread over a range
 
 
94966.png94972.png
 
This broadens the spectral line by an amount (2 Δλ). It is called Doppler broadening. The Doppler broadening is proportional to v, which in turn is proportional to 94978.png where T is the temperature in Kelvin.

Radar

Radar is a system for locating distant object by means of reflected radio waves, usually of microwave frequencies. Radar is used for navigation and guidance of aircraft, ships, etc.
 
Radar employs the Doppler effect to distinguish between stationary and moving targets. The change in frequency between transmitted and received waves is measured. If v is the velocity of the approaching target, then the change in frequency is 94990.png. (The factorof 2 arises due to refection of waves). For a receding target 94996.png. (The minus sign indicates decrease in frequency).




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